Rename AuthMode to Backend, fix LiteLLM variant typo, add image update alerts, clean up Settings

- Fix serde deserialization error: TypeScript sent "lit_llm" but Rust expected "lite_llm"
- Rename AuthMode enum to Backend across Rust and TypeScript (with serde alias for backward compat)
- Add container image update checking via registry digest comparison
- Improve Settings page: fix image address display spacing, remove per-project auth section
- Update UI labels from "Auth" to "Backend" throughout

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

app/src/components/projects/ProjectCard.test.tsx

@@ -57,7 +57,7 @@ const mockProject: Project = {
   paths: [{ host_path: "/home/user/project", mount_name: "project" }],
   container_id: null,
   status: "stopped",
-  auth_mode: "anthropic",
+  backend: "anthropic",
   bedrock_config: null,
   allow_docker_access: false,
   ssh_key_path: null,